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Thread ID: 50661	2004-10-28 06:23:00	Maths Revision	Gum Digger (5187)	Press F1

Post ID	Timestamp	Content	User
285504	2004-10-29 09:34:00	Growly, > As you incorrectly calculated, this is > 2992/(1.105^2)=$2450.40. You can't work out the interest this way. This is because it is not a lump sum interest, it is a compounding interest. What you need to do is take off the second year's interest, then the first years. [b]$2992 / 1.105 = $2707.69 $2707.69 / 1.105 = $2450.40	Bletch (244)
285505	2004-10-29 09:36:00	Does someone want me to do a really simple, step by step analysis of the problem which shows how to get all of the info out of the original question? I can post this on the thread tonight if ppl want.	Bletch (244)
285506	2004-10-29 09:37:00	Oh had another thought, maybe his parents are saving the money for him so he can pay a lump sum each year for his interest and final payments? so he has the money already, and no panics to find it later? beetle ?:|	beetle (243)
285507	2004-10-29 09:41:00	He doesn't pay two lump sums. The only lump sum he pays is at the end, including 2 years compounding interest. He can't be getting the parents to save the money for him, because it says that he pays back the 70% in two ways. Therefore the parents cannot be saving for the lump sum	Bletch (244)
285508	2004-10-29 10:35:00	You seem right Bletch, and I can follow your logic. However, it seems blatently obvious to me that if you are the only one here who can even understand what the question is asking, then it is badly worded. Any question that can cause so much debate over the meaning is very poorly constructed. I don't really think that making the question confusing is a fair way to test common sense (if that's what they were playing at, if not they were just dumb). In fact (and my [highly skilled] maths teacher agrees) a lot of NCEA 1 questions are poorly worded and ambiguous. In fact there was one Excellence question made, last year I beleive, that 0% of NZ got correct. That is of course rounded down from 0.1823865 or something, but it is still showing how bad a question it must have been (a much higher percentage is supposed to get excellence). I didn't get this one at the start either, and I consider myself not bad at maths. I agree with Growly on this one. George	george12 (7)
285509	2004-10-29 10:40:00	George, I fully agree with you. A question like this does not belong in a level 1 NCEA test. Do you know if it was an E, M, or A question? Here is the full explaination, which I hope will help you understand it. Here is the full explaination of the problem. All answers rounded to 2 decimal places. John bought a car. STUFF WE KNOW: 1) He pays parents $45/month for 2 years. This is $45 * 24 months. This payment MUST go towards the 70%, because it says that he paid (not borrowed) the 30%. The total amount was $1080. 2) He pays a lumpsum to the car dealer. This sum is $2992, and consists of: 70% of car + 10.5% interest + another 10.5% interest. 3) He has already paid off 30% of the car. Summary of what we know: 1) he paid parents $1080. 2) He paid the dealer $2992 lumpsum. 3) He paid the dealer a lumpsum deposit of 30% of the original car price. STEP ONE - REMOVE INTEREST FROM LUMP SUM $2992 includes compounding interest, so we must remove 10.5% for each time interest was calculated (i.e. we can't simply take off 10.5% * 2) 100% = 100/100 = 1 10.5% = 10.5/100 = 0.105 1 + 0.105 = 1.105 $2995 / 1.105 = $2710.41 (this removes the second year of interest) $2710.41 /1.105 = $2452.86 (this removes the first year of interest) Therefore the lum sum without interest is $2452.86. This is 70% of the total cost of the car, less what he paid his parents. STEP TWO - THE CONFUSING BIT We know this because the problem states that he paid the borrowed money back in two ways - to his parents ($1080) and the rest as a lump sum to the dealer. The problem occurs when we try to consider what happened to the money he paid his parents. Obviously the money was not paid to the dealer immediately, because John had an agreement in which he paid nothing for 2 years. However, the problem fails to tell us whether the money he pays his parents is included in the lump sum payment. Using common sense, we can determine that the money paid to the parents is not part of the lumpsum payment, because it cannot be a separate payment method if it is merely an accessory to the another method. The money paid to the parents obviously is for the car dealer, as it is stated as a payment option. Therefore, the payments are separate from the lump sum payment, but still go towards paying off the car. As nothing is mentioned about interest in relation to these payments, we can safely assume that this is something we do not have to worry about. STEP THREE - WHERE THE MONEY WENT 30% was paid as a deposit $2452.86 was paid as a lump sum $1080 was paid to the parents, and then somehow got to the car dealer. 10.5% interest was calculated on two occasions. As we have removed it from the lump sum, and it is not relevant to the original price of the car, we can safely forget about it. STEP FOUR - BRINGING IT ALL TOGETHER The money is divided as follows: 30% - initial deposit $2452.86 lump sum $1080 paid to parents To work out the cost of the car, we first add the lump sum to the money paid to the parents: $2452.86 + $1080 = $3532.86. Because this is only 70% of the price of the car, we then divide it by 70/100 (0.7). $3532.86 / 0.7 = $5046.94 This gives us 100% of the car's original cost, before interest. STEP FIVE - THE FINAL ANSWER The final answer is $5046.94.	Bletch (244)
285510	2004-10-29 10:57:00	That was a beatiful explanation. You should be a maths teacher :). > Do you know if it was an E, M, or A question? I would guess 'E'. I do understand that the question is possible, and in fact with a ... little bit of help ... anyone can understand it. But when I first saw it I didn't get it, Growly didn't get it, in fact nobody but you did. For that you deserve congratulations, but that is not the point. Out of curiosity (if you don't mind), what year are you in (if you're at school)? Because I imagine you might be in a much higher year than Level 1, in which case nobody here doing Level 1 got the question correct. Do you think NZQA test their questions? Or just write them and hope they work? George	george12 (7)
285511	2004-10-29 11:03:00	I am in year 12 (NCEA Level 2). From what I have seen of level 1 NCEA questions, I think that the people from NZQA don't test them, or if they do then they must have very narrow thinking.	Bletch (244)
285512	2004-10-29 11:15:00	It's rather strange: You would think that they would test the questions, it seems absurd that they might not, but at the same time if they do test one wonders how some of the questions I've seen slip through. Perhaps the people that write them check them too. "I don't even need to read the question, I know it off by heart. After all, I did write the bloody thing!" - Some NZQA Guy Now that would explain some things. George	george12 (7)
285513	2004-10-29 11:19:00	Nice quote, lol!:D What I think they should do is test them on a sample of students (maybe 200 or so) and see how the students manage. If there is mass confusion, then something is obviously wrong with the question.	Bletch (244)
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